Question

What is the range of g(x) = |x + 3| + 2? A. [-3, ∞) B. (-∞, 2] C. [2, ∞) D. (-∞, ∞)

Answer 1

• C. [2, + ∞)

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Given function:

• g(x) = | x + 3| + 2

We know that absolute value is non-negative, hence |x + 3| has a minimum value of 0 when x = - 3. Then the function has a minimum value of 2.

The range is the set of output values. As we see given function has a minimum value of 2 and no maximum value.

It can be shown as:

• g ∈ [2, + ∞)

The matching choice is C.